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C112×A5 #20300133

order7260
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC112×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC112A5
commutator, hypocenterA5C112
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C112

126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

605 conjugacy classes — view the full character table.

Relationships

derived subgroup ofA5×#10597243, A5×#10597244, A5×#10597245
socle ofC11×C11⋊C5×A5, A5×#10597243, A5×#10597244, …
maximal subgroup ofC3×C112×A5, A5×C112⋊C3, C5×C112×A5, …
maximal normal subgroup ofC3×C112×A5, A5×C112⋊C3, C5×C112×A5, …
maximal quotient ofC3×C112×A5, C5×C112×A5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 233);